标题： 改进的几何自一致性图拉普拉斯算子 显示英文标题

标题： Improved graph Laplacian via geometric self-consistency

摘要： 我们研究了流形学习算法中用于构造图拉普拉斯的核带宽设置问题。利用流形几何（由黎曼度量表示）与拉普拉斯-贝尔特拉米算子之间的联系，我们通过优化拉普拉斯保留数据几何结构的能力来确定带宽。实验表明，这种方法是有效且鲁棒的。 显示英文摘要

摘要： We address the problem of setting the kernel bandwidth used by Manifold Learning algorithms to construct the graph Laplacian. Exploiting the connection between manifold geometry, represented by the Riemannian metric, and the Laplace-Beltrami operator, we set the bandwidth by optimizing the Laplacian's ability to preserve the geometry of the data. Experiments show that this principled approach is effective and robust.